Speed, Time and Events: How to Keep Up?

[rajeshmarndi]

as we increase our speed, time goes slow for us, does it mean we will be left behind in times only or as time goes,do we observe the same event that has been observed by those who were ahead than us bcoz of their speed slower than us.

or it depends what happens at our present time. Also how do we define present ?

 

[ghwellsjr]

We can only observe what is happening at our location at the present time. When we see something happening at a distant location, we are seeing it after the light from that situation travels through space to us. Since everyone measures the speed of light relative to themselves as the same constant value, this means that two people traveling with respect to each other can have a different opinion of how long it took for the light to get to them.

This is because we cannot directly observe the transit of light. We cannot tell where it is at any particular time. The only way we can measure the speed of light is with a round-trip experiment. We place a mirror a measured distance away and time how long it takes for a flash of light we emit to travel to the mirror and get back to us. But we cannot measure whether it took the same amount of time to get to the mirror as it took for the light to get from the mirror back to us.

To resolve this problem, Einstein came up with the idea that we can assume that the time it took for the light to get to the mirror is equal to the time it took for the light to get back to us. And so he established the concept of a Frame of Reference in which we define the times for distant events according to this synchronization convention. But this means that different inertial observers traveling with respect to each other will assign different values to the times and locations for the same event.

A Frame of Reference is nothing more than a coordinate system with four parameters, one for time and three for the x, y and z components of the location. The values of these four parameters constitute an "event". In Special Relativity, when we talk about an "event" we mean those four parameters as defined according to a given Frame of Reference. So it shouldn't be surprising that all four of those parameters could have different values for the same event in different Frames of Reference, should it? In fact, there is a way to calculate what those four values are in one FoR if you know what they are in another FoR. It's called the Lorentz Transform.

So when we see that the values for the times of events are different in different Frames of Reference, this should cause us no alarm or concern, it's nothing more than the way we have decided to define the times according to those different Frames of Reference. It doesn't mean that anything different is happening in actuality.

 

[rajeshmarndi]

But we cannot measure whether it took the same amount of time to get to the mirror as it took for the light to get from the mirror back to us.

what makes you to say that the time may not be same.

It doesn't mean that anything different is happening in actuality.

you mean to say event doesn't actually happen at different times in different inertial frame but actually happens simultaneously, its only the delay in light that reaches them.

 

[ghwellsjr]

But we cannot measure whether it took the same amount of time to get to the mirror as it took for the light to get from the mirror back to us.

what makes you to say that the time may not be same.

Well, I'm not the one that is saying it, Einstein said it. You should read his 1905 paper.

But the reason is that two different observers in relative motion will disagree on whether the times are the same. If they are both making their own measurement of the speed of light with their own light source, mirror and timer, they will each measure the round-trip speed of light to be the same value as what the other one measures but if they also each assume that the two parts of the trip are equal for themselves, they will have to say that it is unequal for the other person. That's just the way nature works. Do you believe this?

It doesn't mean that anything different is happening in actuality.

you mean to say event doesn't actually happen at different times in different inertial frame but actually happens simultaneously, its only the delay in light that reaches them.

Simultaneity has no meaning when you are talking about a single event as defined differently according to two different Frames of Reference. I'm saying that something is happening out there in the real world. Nothing changes just because we say that it's location is 1, 2, 3 at time 4 when using the coordinates from one FoR, or location 5, 6, 7 at time 8 using a different set of coordinates from another FoR. And that's because we cannot know what the delay is in the light that we see of the remote event.

 

[bobc2]

as we increase our speed, time goes slow for us, ...?

This comment caught my attention, then I remembered WannabeNewton's post following a similar post.

WannabeNewton: "...time goes neither 'slower' or 'faster' in your own frame of reference..."

[Edit] Now, I found WannabeNewton's exact post:

Not quite correct. In your reference frame time never passes "faster" or "slower" for you. Remember that in your reference frame you are at rest so the components of your 4- velocity are zero except for the one corresponding to the time basis. However, other objects that are not at rest relative to you will experience a time dilation as measured in your frame.